Question

If x and y are inversely proportional, find the values of x₁, x₂, y₁ and y₂ in the table given below:

x	8	x1	16	x2	80
y	y1	4	5	2	y2

Answer 1

$\mathrm{Since}x\mathrm{and}y\mathrm{are}\mathrm{inversely}\mathrm{proportional},xy\mathrm{must}\mathrm{be}\mathrm{a}\mathrm{constant}.$
$$\begin{gathered} \mathrm{Therefore},8\times y_1=x_1\times 4=16\times 5=x_2\times 2=80\times y_2 \\ \mathrm{Now},16\times 5=8\times y_1 \\ \Rightarrow \frac{80}{8}=y_1 \\ \therefore y_1=10 \\ 16\times 5=x_1\times 4 \\ \Rightarrow \frac{80}{4}=x_1 \\ \therefore x_1=20 \\ 16\times 5=x_2\times 2 \\ \Rightarrow \frac{80}{2}=x_2 \\ \therefore x_2=40 \\ 16\times 5=80\times y_2 \\ \Rightarrow \frac{80}{80}=y_2 \\ \therefore y_2=1 \\ \mathrm{Hence},y_1=10,x_1=20,x_2=40\mathrm{and}{y}_2=1 \end{gathered}$$